UML States allow for a separation into concurrent regions but it seems as if these separations are always horizontal. I figure that it should be possible to have vertical region separators in a State but I cannot find how. Help is appreciated.

Yes. 14.2.4.3 of the UML specs show such a vertical division. I guess it's some shortcoming of EA that is just has horizontal divisions. You might as for a new feature (Support section bottom right of this page).